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Manager  Joined: 06 Feb 2010
Posts: 138
Schools: University of Dhaka - Class of 2010
GPA: 3.63
WE: Business Development (Consumer Products)
In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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5
2 00:00

Difficulty:   25% (medium)

Question Stats: 81% (02:14) correct 19% (03:00) wrong based on 209 sessions

HideShow timer Statistics In the figure above, the area of square region PRTV is 81, and the ratio of the area of square region XSTU to the area of square region PQXW is 1 to 4. What is the length of segment RS?

A. 5
B. 5.5
C. 6
D. 6.5
E. 7

Attachment: Untitled.png [ 7.1 KiB | Viewed 6452 times ]

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Originally posted by monirjewel on 09 Nov 2010, 01:08.
Last edited by Bunuel on 16 Oct 2018, 01:29, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 58390
Re: In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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8
2 In the figure above, the area of square region PRTV is 81, and the ratio of the area of square region XSTU to the area of square region PQXW is 1 to 4. What is the length of segment RS?
A. 5
B. 5.5
C. 6
D. 6.5
E. 7

As the area of square region PRTV is 81 then $$RT^2=81$$ --> $$RT=9$$;

The area of square region $$PQXW=QX^2=RS^2$$ and the area of square region $$XSTU=ST^2=(9-RS)^2$$;

Given: $$\frac{(9-RS)^2}{RS^2}=\frac{1}{4}$$ --> $$\frac{9-RS}{RS}=\frac{1}{2}$$ --> $$RS=6$$.

Or: as the ratio of the areas of squares is the square of the ratio of their sides then $$\frac{ST}{RS}=\frac{9-RS}{RS}=\frac{1}{2}$$ --> $$RS=6$$.
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Manager  Joined: 01 Nov 2010
Posts: 111
Location: Zürich, Switzerland
Re: In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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(ST)^2/(QX)^2 = 1/4
So, QX=RS=2ST
since- RT=9(total area of PRTV=81), RT= 3ST.
So ST=3 and RS=6

Manager  S
Joined: 20 Apr 2010
Posts: 187
WE 1: 4.6 years Exp IT prof
Re: In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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1
If the area is 1:4 than the sides will be 1:2
since the total length is 9 (RS+ST) hence it is (3+6) since RS is the Bigger in length therefore,RS = 6
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Manager  Joined: 17 Dec 2010
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Re: In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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I don't agree with the answer "D" - I think it's C

PRTV is a square, with area of 81 => RT = 9

RT = RS + ST = 9

RS^2 = 4ST ^ 2
=> RS = 2ST

=>3ST = 9
=> ST = 3

=> RS = 6

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Re: In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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RT=9 since area of square is 81

Let RS=x and ST=9-x

Ratio of the area of squares is 1:4
Hence x^2 = 4 (9-x)^2
Hence x = 2(9-x)
3x = 18 ... x=6

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Re: In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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_________________ Re: In the figure above, the area of square region PRTV is 81, and the rat   [#permalink] 16 Oct 2018, 01:29
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